. . . "Die Shannon-Zerlegung oder Shannon-Expansion (benannt nach Claude Elwood Shannon) stellt eine M\u00F6glichkeit dar, boolesche Funktionen mithilfe ihrer sogenannten Kofaktoren darzustellen. Die mathematische Aussage \u00FCber diese Zerlegung wird auch als Entwicklungssatz von Shannon bezeichnet. Obwohl der Satz nach Shannon benannt ist, der ihn erstmals 1949 verwendete, wurde er bereits etwa hundert Jahre zuvor von George Boole aufgestellt."@de . "May 2019"@en . . "L'expansion de Shannon est, en logique, la d\u00E9composition d'une \u00E9quation bool\u00E9enne selon une ou plusieurs variables principales. Elle consiste en l'identit\u00E9 suivante, vraie quelle que soit la fonction : o\u00F9 est une formule bool\u00E9enne, est une variable, est la n\u00E9gation de , et les formules et sont obtenus \u00E0 partir de en affectant \u00E0 et respectivement."@fr . "Boole's expansion theorem"@en . . . . . "Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: , where is any Boolean function, is a variable, is the complement of , and and are with the argument set equal to and to respectively. The terms and are sometimes called the positive and negative Shannon cofactors, respectively, of with respect to . These are functions, computed by restrict operator, and (see valuation (logic) and partial application)."@en . . . . . "Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: , where is any Boolean function, is a variable, is the complement of , and and are with the argument set equal to and to respectively. The terms and are sometimes called the positive and negative Shannon cofactors, respectively, of with respect to . These are functions, computed by restrict operator, and (see valuation (logic) and partial application). It has been called the \"fundamental theorem of Boolean algebra\". Besides its theoretical importance, it paved the way for binary decision diagrams (BDDs), satisfiability solvers, and many other techniques relevant to computer engineering and formal verification of digital circuits.In such engineering contexts (especially in BDDs), the expansion is interpreted as a if-then-else, with the variable being the condition and the cofactors being the branches ( when is true and respectively when is false)."@en . . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0435\u043C \u0428\u0435\u043D\u043D\u043E\u043D\u0430 \u0438\u043B\u0438 \u0434\u0435\u043A\u043E\u043C\u043F\u043E\u0437\u0438\u0446\u0438\u0435\u0439 \u0428\u0435\u043D\u043D\u043E\u043D\u0430 \u043F\u043E \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043C\u0435\u0442\u043E\u0434 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u044F \u0431\u0443\u043B\u0435\u0432\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u043E\u0442 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0445 \u0432 \u0432\u0438\u0434\u0435 \u0441\u0443\u043C\u043C\u044B \u0434\u0432\u0443\u0445 \u043F\u043E\u0434\u0444\u0443\u043D\u043A\u0446\u0438\u0439 \u043E\u0442 \u043E\u0441\u0442\u0430\u043B\u044C\u043D\u044B\u0445 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0445. \u0425\u043E\u0442\u044F \u044D\u0442\u043E\u0442 \u043C\u0435\u0442\u043E\u0434 \u0447\u0430\u0441\u0442\u043E \u043F\u0440\u0438\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442 \u041A\u043B\u043E\u0434\u0443 \u0428\u0435\u043D\u043D\u043E\u043D\u0443, \u043D\u043E \u0411\u0443\u043B\u044C \u0434\u043E\u043A\u0430\u0437\u0430\u043B \u0435\u0433\u043E \u0433\u043E\u0440\u0430\u0437\u0434\u043E \u0440\u0430\u043D\u044C\u0448\u0435, \u0430 \u0441\u0430\u043C\u0430 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E\u0441\u0442\u044C \u0442\u0430\u043A\u043E\u0433\u043E \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u043F\u043E \u043B\u044E\u0431\u043E\u0439 \u0438\u0437 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439 \u043D\u0435\u043F\u043E\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043D\u043D\u043E \u0432\u044B\u0442\u0435\u043A\u0430\u0435\u0442 \u0438\u0437 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E\u0441\u0442\u0438 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044F \u043B\u044E\u0431\u043E\u0439 \u0431\u0443\u043B\u0435\u0432\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u0441 \u043F\u043E\u043C\u043E\u0449\u044C\u044E \u0442\u0430\u0431\u043B\u0438\u0446\u044B \u0438\u0441\u0442\u0438\u043D\u043D\u043E\u0441\u0442\u0438."@ru . "1121119300"^^ . "7884"^^ . . . "2733707"^^ . "\u9999\u519C\u5C55\u5F00"@zh . "\u0420\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u0428\u0435\u043D\u043D\u043E\u043D\u0430"@ru . "Die Shannon-Zerlegung oder Shannon-Expansion (benannt nach Claude Elwood Shannon) stellt eine M\u00F6glichkeit dar, boolesche Funktionen mithilfe ihrer sogenannten Kofaktoren darzustellen. Die mathematische Aussage \u00FCber diese Zerlegung wird auch als Entwicklungssatz von Shannon bezeichnet. Obwohl der Satz nach Shannon benannt ist, der ihn erstmals 1949 verwendete, wurde er bereits etwa hundert Jahre zuvor von George Boole aufgestellt."@de . . . "Shannon-Zerlegung"@de . "\u9999\u519C\u5C55\u5F00\uFF08\u82F1\u8A9E\uFF1AShannon's expansion\uFF09\uFF0C\u6216\u79F0\u9999\u519C\u5206\u89E3\uFF08Shannon decomposition\uFF09\u662F\u5BF9\u5E03\u5C14\u51FD\u6570\u7684\u4E00\u79CD\u53D8\u6362\u65B9\u5F0F\u3002\u5B83\u53EF\u4EE5\u5C06\u4EFB\u610F\u5E03\u5C14\u51FD\u6570\u8868\u8FBE\u4E3A\u5176\u4E2D\u4EFB\u4F55\u4E00\u4E2A\u53D8\u91CF\u4E58\u4EE5\u4E00\u4E2A\u5B50\u51FD\u6570\uFF0C\u52A0\u4E0A\u8FD9\u4E2A\u53D8\u91CF\u7684\u53CD\u53D8\u91CF\u4E58\u4EE5\u53E6\u4E00\u4E2A\u5B50\u51FD\u6570\u3002 \u4F8B\u5982\uFF1A \u53EF\u4EE5\u62BD\u53D6\u5176\u4E2D\u7684\u53D8\u91CF \u53CA\u5176\u53CD\u53D8\u91CF \uFF08 \u53D6\u53CD\uFF09\uFF0C\u800C\u5F97\u5230 \u5BF9\u903B\u8F91\u51FD\u6570\u4F7F\u7528\u9999\u519C\u5C55\u5F00\uFF0C\u5C31\u53EF\u4EE5\u4F7F\u7528\u62BD\u53D6\u7684\u53D8\u91CF\u4F5C\u4E3A\u4E00\u4E2A\u9009\u62E9\u4FE1\u53F7\uFF0C\u7136\u540E\u7528\u6570\u636E\u9009\u62E9\u5668\u6765\u5B9E\u73B0\u8BE5\u51FD\u6570\u3002"@zh . . . . "In elettronica digitale il teorema di Shannon \u00E8 un importante teorema riguardante le funzioni booleane principalmente usato per scomporre una funzione complessa in funzioni pi\u00F9 semplici o per ottenere un'espressione canonica da una tabella della verit\u00E0 o da un'espressione non canonica. Nonostante sia attribuito a Claude Shannon, il teorema \u00E8 stato enunciato per primo da George Boole."@it . . . . . . . . . . . . . . . . . "\u9999\u519C\u5C55\u5F00\uFF08\u82F1\u8A9E\uFF1AShannon's expansion\uFF09\uFF0C\u6216\u79F0\u9999\u519C\u5206\u89E3\uFF08Shannon decomposition\uFF09\u662F\u5BF9\u5E03\u5C14\u51FD\u6570\u7684\u4E00\u79CD\u53D8\u6362\u65B9\u5F0F\u3002\u5B83\u53EF\u4EE5\u5C06\u4EFB\u610F\u5E03\u5C14\u51FD\u6570\u8868\u8FBE\u4E3A\u5176\u4E2D\u4EFB\u4F55\u4E00\u4E2A\u53D8\u91CF\u4E58\u4EE5\u4E00\u4E2A\u5B50\u51FD\u6570\uFF0C\u52A0\u4E0A\u8FD9\u4E2A\u53D8\u91CF\u7684\u53CD\u53D8\u91CF\u4E58\u4EE5\u53E6\u4E00\u4E2A\u5B50\u51FD\u6570\u3002 \u4F8B\u5982\uFF1A \u53EF\u4EE5\u62BD\u53D6\u5176\u4E2D\u7684\u53D8\u91CF \u53CA\u5176\u53CD\u53D8\u91CF \uFF08 \u53D6\u53CD\uFF09\uFF0C\u800C\u5F97\u5230 \u5BF9\u903B\u8F91\u51FD\u6570\u4F7F\u7528\u9999\u519C\u5C55\u5F00\uFF0C\u5C31\u53EF\u4EE5\u4F7F\u7528\u62BD\u53D6\u7684\u53D8\u91CF\u4F5C\u4E3A\u4E00\u4E2A\u9009\u62E9\u4FE1\u53F7\uFF0C\u7136\u540E\u7528\u6570\u636E\u9009\u62E9\u5668\u6765\u5B9E\u73B0\u8BE5\u51FD\u6570\u3002"@zh . . . . . . . "y"@en . "\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0435\u043C \u0428\u0435\u043D\u043D\u043E\u043D\u0430 \u0438\u043B\u0438 \u0434\u0435\u043A\u043E\u043C\u043F\u043E\u0437\u0438\u0446\u0438\u0435\u0439 \u0428\u0435\u043D\u043D\u043E\u043D\u0430 \u043F\u043E \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043C\u0435\u0442\u043E\u0434 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u044F \u0431\u0443\u043B\u0435\u0432\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u043E\u0442 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0445 \u0432 \u0432\u0438\u0434\u0435 \u0441\u0443\u043C\u043C\u044B \u0434\u0432\u0443\u0445 \u043F\u043E\u0434\u0444\u0443\u043D\u043A\u0446\u0438\u0439 \u043E\u0442 \u043E\u0441\u0442\u0430\u043B\u044C\u043D\u044B\u0445 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0445. \u0425\u043E\u0442\u044F \u044D\u0442\u043E\u0442 \u043C\u0435\u0442\u043E\u0434 \u0447\u0430\u0441\u0442\u043E \u043F\u0440\u0438\u043F\u0438\u0441\u044B\u0432\u0430\u044E\u0442 \u041A\u043B\u043E\u0434\u0443 \u0428\u0435\u043D\u043D\u043E\u043D\u0443, \u043D\u043E \u0411\u0443\u043B\u044C \u0434\u043E\u043A\u0430\u0437\u0430\u043B \u0435\u0433\u043E \u0433\u043E\u0440\u0430\u0437\u0434\u043E \u0440\u0430\u043D\u044C\u0448\u0435, \u0430 \u0441\u0430\u043C\u0430 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E\u0441\u0442\u044C \u0442\u0430\u043A\u043E\u0433\u043E \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u043F\u043E \u043B\u044E\u0431\u043E\u0439 \u0438\u0437 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0439 \u043D\u0435\u043F\u043E\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043D\u043D\u043E \u0432\u044B\u0442\u0435\u043A\u0430\u0435\u0442 \u0438\u0437 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E\u0441\u0442\u0438 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044F \u043B\u044E\u0431\u043E\u0439 \u0431\u0443\u043B\u0435\u0432\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u0441 \u043F\u043E\u043C\u043E\u0449\u044C\u044E \u0442\u0430\u0431\u043B\u0438\u0446\u044B \u0438\u0441\u0442\u0438\u043D\u043D\u043E\u0441\u0442\u0438."@ru . . "Expansion de Shannon"@fr . . . "Teorema di Shannon (elettronica)"@it . "In elettronica digitale il teorema di Shannon \u00E8 un importante teorema riguardante le funzioni booleane principalmente usato per scomporre una funzione complessa in funzioni pi\u00F9 semplici o per ottenere un'espressione canonica da una tabella della verit\u00E0 o da un'espressione non canonica. Nonostante sia attribuito a Claude Shannon, il teorema \u00E8 stato enunciato per primo da George Boole."@it . . "L'expansion de Shannon est, en logique, la d\u00E9composition d'une \u00E9quation bool\u00E9enne selon une ou plusieurs variables principales. Elle consiste en l'identit\u00E9 suivante, vraie quelle que soit la fonction : o\u00F9 est une formule bool\u00E9enne, est une variable, est la n\u00E9gation de , et les formules et sont obtenus \u00E0 partir de en affectant \u00E0 et respectivement."@fr . . . .